Embodied Mathematics

As a result of my return to my academic research program (more on this later), I recently picked up Lakoff and Nunez’s Where Mathematics Comes From: How the Embodied Mind Brings Mathematics Into Being and was reading about the what a point is. Having studied math through differential equations (when I stopped the formal study of math–as a freshman in college), I thought I knew what a point was. . . . But it turns out that there are two approaches to math which envisions the point as a completely different phenomenon: one involves viewing space as continuous and comes naturally to us, given our experience of 3-D space with an embodied mind. The other involves the “discretizing” program that started in the 19th century and has determined the direction of mathematics ever since. This latter approach actually comes about by means of metaphoric blends whereby two differing “image schemas” are blended together to allow for a completely new understanding.

Now I know many people’s eyes glaze over when one mentions mathematics, but it should come as some comfort to know that we draw upon our “embodied mind” to understand these concepts and that we actually have no other choice than to do so! Knowing how our minds work with these fundamental metaphors could help us learn how to be more creative in the future: by playing with these metaphors, we can create new metaphorical blends which can lead to new insights and fresh perspectives. This is one point of deconstruction as a philosophical approach, at least how I understand it and had it presented to me during various graduate courses at the University of Florida in the late 1980s and early 1990s. This leads to my reason for looking at this book at the moment: I’m investigating mathematical conceptions of space to see if there might be a way to re-think the 3-D world of virtual reality, which, of course, relies in an analogical way upon our “continuous” and natural understanding of space but which doesn’t have to be confined to the limitations of real space. This might lead to new insights into how to store information in such spaces.